Image watermarking based on sequency and wavelet transforms

ABSTRACT

This invention is a new approach for the image watermarking in the wavelet transform domain based on sequency of the host and watermark image. For each sub-band a first transform level of the host image is thresholded and binarized. Sequencies of thresholded and binarized data host image are compared with sequencies of the discrete wavelet transformed watermark image to form a watermarking sequency mask. The watermarked wavelet domain data is formed by combining data elements of the discrete wavelet transformed host image with corresponding data elements of the wavelet transformed watermark image as filtered by the watermarking mask. A reverse process can extract the watermark with a high degree of accuracy even after attack upon the watermarked host image.

CLAIM OF PRIORITY

This application claims priority under 35 U.S.C. 119(e)(1) to U.S.Provisional Application No. 60/752,583 filed Dec. 21, 2005.

TECHNICAL FIELD OF THE INVENTION

The technical field of this invention is image watermarking.

BACKGROUND OF THE INVENTION

Watermarking of the multimedia contents is of prime importance forclaiming and establishing ownership. An image watermark is data added tothe image data. This added data is included in such a way that the imagequality is not degraded. Later extraction tools may be applied to theimage data to recover the watermark. The recovered watermark is evidenceof the original ownership claim to the image.

Most of watermarking techniques are vulnerable to the attacks or arepoorly extracted after the attacks. Images are very common in multimediacontents and need a robust watermarking scheme that can withstand theattacks and at the same time have a recognizable extracted watermark.

In recent years, image watermarking has been a very active area ofresearch and industry. Various techniques have been used for imagewatermarking in the spatial domain, the transform domain and the spreadspectrum domain.

SUMMARY OF THE INVENTION

This invention is a new sequency and wavelet transform basedwatermarking technique. The inventive technique is more robust inresponse to attacks like JPEG, Median filtering and blurring. Theinventive technique provides for good extraction of the watermark image.The inventive technique performs very well in terms of subjective(perceptual) and objective (in terms of PSNR) image quality measures.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of this invention are illustrated in thedrawings, in which:

FIG. 1 illustrates the process of watermarking an image and extractingthe watermark from an image subject to attack;

FIG. 2 illustrates in schematic form one level of wavelet decomposition(Prior Art);

FIG. 3 illustrates transformed wavelet data divided into four quadrantsub-bands (Prior Art);

FIG. 4 illustrates further division of a quadrant into smaller bands(Prior Art);

FIG. 5 illustrates a third level division of a subquadrant into yetsmaller bands (Prior Art);

FIG. 6 schematically illustrates the embedding of a watermark in thewavelet and sequency transformed domain of a host image;

FIG. 7 schematically illustrates extracting the watermark from thewatermarked host image;

FIG. 8A is an example 256 by 256 gray scale host image and FIG. 8B is anexample 64 by 64 binary watermark image;

FIG. 9 illustrates the corresponding watermarked image in accordancewith the examples of FIGS. 7A and 7B;

FIGS. 10A to 10D illustrate a comparison of the original watermark imagewith watermark images extracted from watermarked host images subject toJPEG attack of varying quality factors;

FIG. 11 illustrates an example extracted watermark resulting from amedian filtering attack of a watermarked host image;

FIGS. 12A and 12B illustrate the example host image and thecorresponding extracted watermark image subject to for a blurred imageattack; and

FIGS. 13A and 13B illustrate the example host image and thecorresponding extracted watermark image subject a contrast enhanced hostimage attack.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

This invention is a new image watermarking technique based on thesequency of the host and watermark images in the wavelet transformdomain. Sub-bands of the host image are thresholded and converted tobinary format. The row sequency of the sub-bands of these binarysub-bands of the host image represents the threshold crossing (zerocrossings) of the image pixels in the wavelet transform domain.Similarly in the binary discrete wavelet transform (BDWT) domain wherethe watermark image is being de-correlated, the row sequency of eachsub-band represents the zero crossing of the watermark image pixels.

This invention uses these sequencies of host and watermark images todevise a new watermarking technique. In the transform domain, thesequency of each row of respective sub-bands is used to determine asequency dependent mask. This mask facilitates better embedding of thewatermark in the appropriate sequency components in the respectivesub-bands.

This invention is the first use of the sequencies of host and watermarkimages to devise a new robust image watermarking scheme. This inventionis also the first to embed the watermark in the LL band (low frequencysub-band after discrete wavelet transform in 2-dimensions) of the hostimage and maintain the perceptual signal to noise ration (PSNR) and theperceptual quality of the watermarked host image.

This invention uses an Adaptive Parabolic Gain adjustment technique thatenables effective embedding into the sub-bands of the host image.

This invention includes a watermark extraction algorithm. This watermarkextraction algorithm takes into account the impact of attacks on thestatistics of the watermarked image such as autocorrelation change ofthe host due to attack and embedding of the watermark. Experiments onthe new sequency based watermarking algorithm show its robustness toattacks and better normalized correlation (NC). Normalized Correlationis an objective measure and defined as:

$\begin{matrix}{{NC} = \frac{\sum\limits_{i}^{\;}\;{\sum\limits_{j}^{\;}\left( {{W\left( {i,j} \right)}{W^{\prime}\left( {i,j} \right)}} \right)}}{\sum\limits_{i}^{\;}\;{\sum\limits_{j}^{\;}\left( {W\left( {i,j} \right)} \right)^{2}}}} & (1)\end{matrix}$Where: W(i,j) is original watermark image; and W′(i,j) is the extractedwatermark image.

The performance results of this invention are clearly superior toexemplary prior art algorithms. This invention is more robust to JPEGattacks in its class of algorithms and maintains the perceptual qualityof the watermarked host image.

FIG. 1 illustrates the general watermarking problem. Watermark function101 receives a host image H and a watermark W. Watermark function 101embeds the watermark W into the host image H according to the functionΦ(H,W,R). R is the autocorrelation of the sub-band pixels of the hostimage. Watermark function 101 generates a watermarked image H_(W) and aset of side information keys K. Keys K are used in later extraction ofthe watermark. Attack function 102 models the possible attacks on thewatermark image H_(W) according to the function A(H_(Ŵ)|H_(W)). Thisattack results in an image {tilde over (H)}. Watermark extractionfunction 103 extracts the watermark image from the attacked image {tildeover (H)} via function Ψ(H_(Ŵ),K,R). Watermark extraction function 103uses keys K which are available only to the owner of the original imageand not to the attacker. The result is extracted watermark {tilde over(W)}.

In this description: host image H is a matrix of size N by N where eachelement belongs to the set of integers Z of size N; watermark image W isa matrix of size N/4 by N/4 where each element belongs to the set ofintegers Z of size 2 containing elements 0 and 1; R is a correlationmatrix of host image pixels of size N by N where each element belongs tothe set of integers Z of size N; key vector K includes keys K₁, K₂ andK₃; K₁ is a subset of Z_(N/8); K₂ is a subset of Z; and K₃ is a subsetof R₄, which is a set of real numbers or cardinality four.

This application uses the following notation for wavelet transformsegments. X_YZ_(n): where X denotes H for the host image or W for thewatermark image; YZ denotes one of the sub-bands selected from LL, HL,LH or HH; and the subscript n denotes the sub-band number. Thus H_LH₃denotes the level 3 LH sub-band of the host image. These notations willbe more fully described in FIGS. 3 to 5. The subscript w indicates thewatermark image and the subscript h indicates the host image. Thus H_(W)is watermarked host image and Ĥ_(w) is watermarked host image after theattack.

Wavelet encoding of image data transforms the image from a pixel spatialdomain into a mixed frequency and spatial domain. In the case of imagedata the wavelet transformation includes two dimensional coefficients offrequency and scale. FIG. 2 illustrates the basic technique of waveletimage transformation. Wavelet coefficients of the image are computedusing one dimensional wavelet filters using a Daubechies filter for thehost image and a binary wavelet filter for the binary watermark image.This decomposition provides sub-images corresponding to differentresolution levels and orientations. The reconstruction process is thecomplementary process of this decomposition process and done byreversing the steps of the decomposition process. The two dimensionalarray of pixels is analyzed X and Y directions and a set for transformeddata that can be plotted in respective X and Y frequency.

FIG. 2 illustrates one stage of wavelet decomposition. The input isimage matrix 200. Note that this input could be the original image for afirst stage decomposition or the result of a prior stage of waveletdecomposition. The rows of this image matrix are low pass filtered inlow pass filter 210 and high pass filtered in high pass filter 220. Thelow pass result from low pass filter 210 is subjected to a column downsample by a factor of 2 in column down sampler 215. Similarly, the lowpass result from low pass filter 220 is subjected to a column downsample by a factor of 2 in column down sampler 225. Each of these downsampled outputs is similarly processed. Low pass filter 230 low passfilters the output of column down sampler 215. The low pass result fromlow pass filter 230 is subjected to a row down sample by a factor of 2in row down sampler 235. The row down sampled result of row down sampler235 is the LL output sub-band. Low pass filter 240 low pass filters theoutput of column down sampler 215. The low pass result from low passfilter 240 is subjected to a row down sample by a factor of 2 in rowdown sampler 245. The row down sampled result row down sampler 245 isthe LH output sub-band. Low pass filter 250 low pass filters the outputof column down sampler 225. The low pass result from low pass filter 250is subjected to a row down sample by a factor of 2 in row down sampler255. The row down sampled result row down sampler 255 is the HL outputsub-band. Low pass filter 260 low pass filters the output of column downsampler 225. The low pass result from low pass filter 260 is subjectedto a row down sample by a factor of 2 in row down sampler 265. The rowdown sampled result row down sampler 265 is the HH output sub-band. Lowpass filters 210, 230 and 250 and high pass filters 220, 240 and 260 arethe one dimensional wavelet filters noted above.

Each of FIGS. 3 to 5 represents one stage in a multi-scale sub-banddecomposition of an image. FIG. 3 illustrates transformed data 300 withthe upper left corner the origin of the X and Y frequency coordinates.This transformed data is divided into four quadrant sub-bands. Quadrant301 includes low frequency X data and low frequency Y data denoted asLL₁. Quadrant 302 includes low frequency X data and high frequency Ydata denoted LH₁. Quadrant 303 includes high frequency X data and lowfrequency Y data denoted HL₁. Quadrant 304 includes high frequency Xdata and high frequency Y data denoted HH₁.

Organizing the image data in this fashion with a wavelet transformpermits exploitation of the image characteristics for data analysis andmanipulation. It is found that most of the energy of the data is locatedin the low frequency bands. The image energy spectrum generally decayswith increasing frequency. The high frequency data contributes primarilyto image sharpness. When describing the contribution of the lowfrequency components the frequency specification is most important. Theenergy distribution of the image data may be further exploited bydividing quadrant 301 LL₁ into smaller bands. FIG. 4 illustrates thisdivision. Quadrant 301 is divided into subquadrant 311 denoted LL₂,subquadrant 312 denoted LH₂, subquadrant 313 denoted HL₂ and subquadrant314 denoted HH₂. As before, most of the energy of quadrant 301 is foundin subquadrant 311. FIG. 5 illustrates a third level division ofsubquadrant 311 into subquadrant 321 denoted LL₃, subquadrant 322denoted LH₃, subquadrant 323 denoted HL₃ and subquadrant 324 denotedHH₃.

For an n-level decomposition of the image, the lower levels ofdecomposition correspond to higher frequency sub-bands. Level onerepresents the finest level of resolution. The n-th level decompositionrepresents the coarsest resolution. Moving from higher levels ofdecomposition to lower levels corresponding to moving from lowerresolution to higher resolution, the energy content generally decreases.If the energy content of level of decomposition is low, then the energycontent of lower levels of decomposition for corresponding spatial areaswill generally be smaller. There are spatial similarities acrosssub-bands.

This invention uses the sequencies of host and watermark images todevise a new watermarking scheme. In the wavelet transform domain, thesequency of each row of respective sub-bands is used to decide asequency dependent mask. This mask facilitates better embedding of thewatermark in the appropriate sequency components in the respectivesub-bands.

In this invention the sub-band LL₁ of the watermark is embedded in theLL₁ band of the host image. The perceptual signal to noise ratio (PSNR)of the host watermarked image is still within acceptable limits.Experimental results of the new sequency watermarking algorithm showrobustness to attacks and better NC.

This invention uses the sequencies of the binary image for the firsttime. Since the sequency is defined as the number of zero crossing ofthe binary data and represents the zero crossings of the binarysequence, it is a very effective way of exploring and embedding thewatermark in the respective sequency indexed sub-bands of the host imagein the wavelet transformed domain.

FIG. 6 schematically illustrates an example 400 of the watermarking ofthis invention. Host image 401 is wavelet transformed using discretewavelet transform (DWT) into wavelet transformed host image 402. Thisexample uses a Daubechies discrete wavelet transform into three levelwavelet sub-bands LL₃, LH₃, HL₃, HH₃, LH₂, HL₂, HH₁, LH₁, HL₁ and HH₁such as illustrated in FIG. 5. A binary watermark image 411 istransformed using binary discrete wavelet transform (BDWT) into wavelettransformed watermark image 412. In this example the binary watermarkimage is transformed into one level sub-bands LL₁, LH₁, HL₁ and HH₁ suchas illustrated in FIG. 3. In this example host image 401 has dimensionsN by N pixels and binary watermark image has dimension N/4 by N/4pixels.

FIG. 6 illustrates details of process 400 of embedding the W_LL₁sub-band into the H_LL₃ sub-band. The embedding of other sub-bands ofthe watermark image into respective host image sub-bands is similar. Inparticular the W_LH₁, W_HL₁ W_HH₁ sub-bands are embedded into respectiveH_LH₃, H_HL₃ and H_HH₃.

Process 400 next pseudo randomizes (prand) the rows of W_LL₁ (421) asshown in equation (2).P _(rand) :W _(—) LL ₁ →{tilde over (W)} _(—) LL ₁  (2)The seed used in this pseudo randomization generates the key K2.

The next step in process 400 is binarization of sub-band H_LL₃ (422).This involves thresholding the gray scale image. Next process 400calculates the row sequencies S_(h) (423) which are the number ofcrossings over a threshold (zero crossing) of H_LL₃ according toequation (3):

$\begin{matrix}{S_{h} = \left\{ {{{{S_{h}(i)} \in Z_{i}};{i = 1}},{\ldots\mspace{11mu}\frac{N}{8\;}}} \right\}} & (3)\end{matrix}$Similarly process 400 calculates the row sequencies S_(w) (424) of thebinary W_LL₁ according to equation (4):

$\begin{matrix}{S_{w} = \left\{ {{{{S_{w}(i)} \in Z_{i}};{i = 1}},{\ldots\mspace{11mu}\frac{N}{8\;}}} \right\}} & (4)\end{matrix}$These sequencies S_(h) and S_(w) are not unique so first best match isselected. The selected sequency of the watermark image row is excludedin subsequent iterations.

Embedding mask generation 425 sets an embedding mask function ƒ forsub-band H_LL₃ given by:

$\begin{matrix}{{f_{{LL}_{3}} = \left\{ {{f(1)} = \left( {j\text{:}\mspace{11mu}\min{{{S_{h}(i)} - {S_{w}(j)}}}} \right\}} \right\}}{{{\forall{i\mspace{14mu}{and}\mspace{14mu} j}} = 1},\ldots\mspace{11mu},{\frac{N}{8\;}\mspace{14mu}{where}\mspace{14mu} i},{j \in \left\{ {1,\ldots\mspace{11mu},\frac{N}{8\;}} \right\}}}} & (5)\end{matrix}$where: |X| is the Euclidian norm distance measure. The embedding maskingfunction ƒ_(LL) ₃ , generates key K₁ for the sub-band LL₃. Embeddingmask generator 425 performs the transform:ƒ_(LL) ₃ :{tilde over (W)} _(—) LL ₁(i,j)→{tilde over (W)} _(—) LL₁(ƒ_(LL) ₃ (i),j)  (6)

Watermark embedding algorithm 430 operates for W_LL₁ as functionΨ(H,W,R) noted in conjunction with FIG. 1 as follows:Ĥ _(—) LL ₃(i,j)=H _(—) LL ₃(i,j)+α_(LL) ₃ *S(H _(—) R _(LL) ₃(i,j)*{tilde over (W)} _(—) LL ₃(ƒ_(LL) ₃ (i),j)  (7)where: α_(LL) ₃ is a constant watermark strength given by:

$\begin{matrix}\begin{matrix}{\alpha = \left\lbrack {\alpha_{{LL}_{3}},\alpha_{{LH}_{3}},\alpha_{{HL}_{3}},\alpha_{{HH}_{3}}} \right\rbrack^{T}} \\{{= \left\lbrack {2,1,1,1} \right\rbrack^{T}};}\end{matrix} & (8)\end{matrix}$with [x]^(T) the transpose of a column vector x;S(H _(—) R _(LL) ₃ (i,j)=(2*√{square root over (K _(3(LL) ₃ ₎*abs(H _(—)R _(LL) ₃ (i,j)))}{square root over (K _(3(LL) ₃ ₎*abs(H _(—) R _(LL) ₃(i,j)))}+G _(LL) ₃ (i,j),  (9)which is a parabolic function of H_R_(LL) ₃ (i,j); abs(x) is theabsolute value of x;G _(LL) ₃ (i,j)={2*√{square root over (max(H _(—) R _(LL) ₃ (i,j)*K_(3(LL) ₃ ₎)}{square root over (max(H _(—) R _(LL) ₃ (i,j)*K _(3(LL) ₃₎)}+ε}  (10)which is a maximum weight factor of embedding with strength S which isfunction of H_R_(LL) ₃ (i,j); H_R_(LL) ₃ (i,j) is the autocorrelation ofthe pixel (i,j) of the wavelet transformed host image sub-band H_LL₃;abs(x) is absolute value of x; ε is a constant generally equal to 5; thevalue of K_(3(LL) ₃ ₎ is given by:K ₃ =[K _(3(LL) ₃ ₎ ,K _(3(LH) ₃ ₎ ,K _(3(HL) ₃ ₎ ,K _(3(HH) ₃₎]^(T)=[20,10,10,10]^(T);  (11)Partially watermarked wavelet domain image 435 is the result.

The watermarking process proceeds to embed sub-bands W_LH₁, W_HL₁ andW_HH₁ of the watermark image into respective sub-bands H_LH₃, H_HL₃ andH_HH₃ of the host image. Following these watermarking steps results inwatermarked wavelet domain image 440. Performing an inverse DiscreteWavelet Transform (IDWT) on watermarked wavelet domain image 440 resultsin watermarked image 450.

FIG. 7 illustrates process 500 extracting the watermark from watermarkedhost image 450. Original host image 401 is possibly damaged due toattack 102 illustrated in FIG. 1. Process 500 begins with a discretewavelet transform (DWT) of original host image 401 yielding wavelettransformed host image 402. This example uses a Daubechies discretewavelet transform into three level wavelet sub-bands LL₃, LH₃, HL₃, HH₃,LH₂, HL₂, HH₁, LH₁, HL₁ and HH₁ such as illustrated in FIG. 5. Process500 also discrete wavelet transforms (DWT) the watermarked host image450 yielding wavelet transformed watermarked host image 502. Thisexample also uses a Daubechies discrete wavelet transform into threelevel wavelet sub-bands LL₃, LH₃, HL₃, HH₃, LH₂, HL₂, HH₁, LH₁, HL₁ andHH₁ such as illustrated in FIG. 5.

FIG. 7 illustrates details of process 500 of watermark extractionoperating on the H_LL₃ sub-band of wavelet transformed host image 502and the Ĥ_LL₃ sub-band of wavelet transformed watermarked host image 502yielding the Ŵ_LL₁, sub-band of the extracted watermark image. Theextraction of other sub-bands of the watermark image is similar.

Process 510 calculates the weight factor Ŝ from the wavelet transformedwatermarked host image 502 and key K_(3(LL) ₃ ₎. This calculation is asfollows:Ŝ({circumflex over (H)}_(—) R _(LL) ₃ (i,j)=(2*√{square root over(K_(3(LL) ₃ ₎*abs(Ĥ _(—) R _(LL) ₃ (i,j)))}{square root over (K_(3(LL) ₃₎*abs(Ĥ _(—) R _(LL) ₃ (i,j)))}+Ĝ _(LL) ₃ (i,j),  (12)where:Ĝ _(LL) ₃ (i,j)={2*√{square root over (max(Ĥ _(—) R _(LL) ₃ (i,j)*K_(3(LL) ₃ ₎)}{square root over (max(Ĥ _(—) R _(LL) ₃ (i,j)*K _(3(LL) ₃₎)}+ε}  (13)Ĥ_R_(LL) ₃ (i,j) is the autocorrelation of the pixel(i,j) of the wavelettransformed host image sub-band Ĥ_LL₃.

Process 510 then models the effect of the attacks on the watermarkedhost image and decides threshold values in the extraction as follows:ΔĤ _(—) R _(LL) _(s) (i,j)=Ĥ _(—) R _(LL) _(s) (i,j)*H _(—) R _(LL) _(s)(i,j)  (14)Process 510 performs the inverse of equation (7) to obtain {tilde over(W)}_LL₃(ƒ_(LL) ₃ (i),j). This process uses the following thresholds:T₁=0.75 and T₂=1.25M _(LL) ₃ (i,j)=(T ₁+0.75*ΔĤ _(—) R _(LL) ₃ (i,j))/2N _(LL) ₃ (i,j)=(5*T ₂+0.75*ΔĤ _(—) R _(LL) ₃ (i,j))/2; and  (15)R _(LL) ₃ (i,j)=(T ₁−0.75*ΔĤ _(—) R _(LL) ₃ (i,j))/2calculates an intermediate value D_(LL) ₃ as follows:

$\begin{matrix}{D_{{LL}_{3}} = \frac{{abs}\left( {{\hat{H}{\_ LL}_{3}\left( {i,j} \right)} - {{H\_ LL}_{3}\left( {i,j} \right)}} \right)}{\alpha_{{LL}_{3}}*{\hat{S}\left( {\hat{H}{\_ R}_{{LL}_{3}}\left( {i,j} \right)} \right.}}} & (16)\end{matrix}$Individual pixels (i,j) of the extracted watermark image are determinedfrom M_(LL) ₃ (i,j), N_(LL) ₃ (i,j), R_(LL) ₃ (i,j) and D_(LL) ₃ asfollows:If ((D _(LL) ₃ >0 AND M _(LL) ₃ <D _(LL) ₃ >N _(LL) ₃ ) OR (D _(LL) ₃ <0AND R _(LL) ₃ <D _(LL) ₃ >N _(LL) ₃ )Then Ŵ _(—) LL ₁(ƒ_(LL) ₃ (i),j)=1  (17)Else Ŵ _(—) LL ₁(ƒ_(LL) ₃ (i),j)=0Process 510 recovers masking function ƒ using key K₁ as follows:ƒ_(LL) ₃ ⁻¹ :{tilde over (W)} _({circumflex over (—)}) LL ₁(ƒ_(LL) ₃(i),j)→{tilde over (W)} _({circumflex over (—)}) LL ₁(i,j)  (18)Lastly, process 510 undoes the pseudo randomization of the rows of thewatermark image using key K₂ as follows:P _(LL) ₃ ⁻¹ :{tilde over (W)} _({circumflex over (—)}) LL ₁(i,j)→W_({circumflex over (—)}) LL ₁(i,j)  (19)The result is wavelet domain partially extracted watermark 520.

Process 510 repeats these steps to extract the sub-bandsW_({circumflex over (—)})LH₁, W_({circumflex over (—)})HL₁ andW_({circumflex over (—)})HH₁. These sub-bands combined form waveletdomain extracted watermark 525. This is subjected to an inverse binarydiscrete wavelet transform to produce extracted watermark image 530.

FIGS. 7 to 12 illustrate an example host image and watermark. FIG. 8A isa 256 by 256 gray scale image entitled “Lena.” This particular image iswidely used in image experiments. FIG. 8B is 64 by 64 binary watermarkimage of the logo of Texas Instruments Incorporated, the assignee ofthis invention. FIG. 9 illustrates the corresponding watermarked imagein accordance with this invention just described. The perceptual signalto noise ratio (PSNR) of the watermarked host image as illustrated inFIG. 9 calculated as described in Hsu, C. T. and J. L. Wu,“Multiresolution Watermarking for Digital Images,” IEEE Tr. CAS-2, Vol.45, No. 8, August 1998, pp. 1097-1101 is 38.6039 dB. Perceptually thewatermarked host image of FIG. 9 is without many visual artifacts andthere is little deterioration from the original host image.

Table 1 shows the extracted watermark performance evaluated on a NCscale for various JPEG attacks. The extracted NC performance is shownfor various levels of JPEG compression ratio (CR) and quality factor(QF).

TABLE 1 JPEG CR JPEG QF Extracted Watermark NC 2.15 100 0.9034 6.70 800.9020 9.53 60 0.8813 12.05 40 0.8551 17.11 20 0.6519 20.90 10 0.5493FIG. 10 illustrates a comparison of the original watermark image (FIG.10A) with watermark images extracted from JPEG attacked watermarked hostimages of qualify factor (QF) 60 in FIG. 10B, 40 in FIG. 10C and 20 inFIG. 10D.

Table 2 shows extracted watermark performance evaluated on a NC scalefor various levels of median filtering attacks.

TABLE 2 Filter Length Extracted Watermark NC 3 0.67 5 0.5191 7 0.5453 90.5392FIG. 11 illustrates an extracted watermark resulting from a medianfiltering attack of length 3.

Table 3 shows extracted watermark performance evaluated on a NC scalefor various rotation angles of attack.

TABLE 3 Rotation Angle (Degrees) Extracted Watermark NC 0.25 0.5513 0.500.5171 −0.25 0.5815 −0.50 0.5272

FIG. 12 illustrates the example host image (FIG. 12A) and thecorresponding extracted watermark image (FIG. 12B) for a blurred imageattack.

FIG. 13 illustrates the example host image (FIG. 13A) and thecorresponding extracted watermark image (FIG. 13B) for a contrastenhanced host image attack.

This invention uses sequency and the wavelet transforms in a novel imagewatermarking algorithm. The performance results shown in FIGS. 8 to 13demonstrate superior results over the technique described in Hsu, C. T.and J. L. Wu, “Multiresolution Watermarking for Digital Images,” IEEETr. CAS-2, Vol. 45, No. 8, August 1998, pp. 1097-1101. This invention isthe first attempt to embed a watermark is in the LL band of a wavelettransformed host image. In this invention the PSNR and the perceptualquality of the watermarked host image maintains a good value. In thewatermark extraction algorithm of this invention, the impact of theattacks on the statistics of the watermarked image can be taken intoaccount. This invention always demonstrates better results than theexisting algorithms on the basis of NC as the extracted watermarkquality.

1. A method for embedding a binary watermark image into a gray scalehost image comprising the steps of: discrete wavelet transforming thehost image; discrete binary wavelet transforming the watermark image;for each sub-band subb selected from the set of LL, LH, HL and HH of afirst predetermined transform level of the host image and a secondpredetermined transform level to the watermark image thresholding andbinarizing data elements of the corresponding sub-band of the discretewavelet transformed host image, comparing sequencies of thresholded andbinarized data elements of the discrete wavelet transformed host imagewith sequencies of the discrete wavelet transformed watermark image toform a watermarking sequency mask, forming watermarked wavelet domaindata by combining data elements of the corresponding sub-band of thediscrete wavelet transformed host image with data elements of thecorresponding sub-band of the wavelet transformed watermark image asfiltered by the watermarking mask, and inverse discrete transforming thewatermarked wavelet domain data thereby forming a watermarked hostimage.
 2. The method of claim 1, wherein: said step of comparingsequencies generates a sequency key.
 3. The method of claim 1, wherein:said step of comparing sequencies to form a watermarking mask includescalculating a binary host image sub-band sequency as follows:${S_{h} = \left\{ {{{{S_{h}(i)} \in Z_{i}};{i = 1}},{\ldots\mspace{11mu}\frac{N}{8\;}}} \right\}},$calculating a watermark image sub-band sequency as follows:${S_{w} = \left\{ {{{{S_{w}(i)} \in Z_{i}};{i = 1}},{\ldots\mspace{11mu}\frac{N}{8\;}}} \right\}},$forming said embedding mask ƒ as follows:f_(subb) = {f(1) = (j:  min S_(h)(i) − S_(w)(j)}}${{\forall{i\mspace{14mu}{and}\mspace{14mu} j}} = 1},\ldots\mspace{11mu},{\frac{N}{8\;}\mspace{14mu}{where}\mspace{14mu} i},{j \in \left\{ {1,\ldots\mspace{11mu},\frac{N}{8\;}} \right\}},$where: |X| is the Euclidian norm distance measure, and transforming thewatermark image as follows:ƒ_(subb) :W_subb(i,j)→W_sub(ƒ_(subb)(i),j) where: W_subb(i,j) is thewatermark image; and W_subb(ƒ_(subb)(i),j) is the transformed watermarkimage after sequency mask transformation.
 4. The method of claim 3,wherein: said step of comparing sequencies to form a watermarking maskgenerates a mask key.
 5. The method of claim 1, wherein: said step offorming watermarked wavelet domain data includes combining the hostimage and the watermarking mask as followsĤ_subb( i,j)=H_subb(i,j)+α_(subb) *S(H _(—) R _(subb)(i,j)*{tilde over(W)}_subb(ƒ _(subb)(i),j) where: H_subb(i,j) is the discrete wavelettransformed host image for the sub-band subb; α_(subb) is a constantwatermark strength for the respective sub-band given by:α_(subb)=[α_(LL) ₃ ,α_(LH) ₃ ,α_(HL) ₃ ,α_(HH) ₃ ]^(T),=[2,1,1,1]^(T) with [x]^(T) the transpose of a column vector x;S(H _(—) R _(subb)(i,j)=(2*√{square root over (K _(subb)*abs(H _(—) R_(subb)(i,j)))}+G _(subb)(i,j), which is a parabolic function ofH_R_(subb)(i,j); abs(x) is the absolute value of x;G _(subb)(i,j)={2*√{square root over (max(H _(—) R _(subb)(i,j)*K_(3sub))}+ε} which is a maximum weight factor of embedding with strengthS which is function of H_R_(subb)(i,j); H_R_(subb)(i,j) is theautocorrelation of the pixel(i,j) of the wavelet transformed host imagesub-band H_subb; abs (x) is absolute value of x; ε is a predeterminedconstant; K₃ is given by:K₃=[K_(3(LL)),K_(3(LH)),K_(3(HL)),K_(3(HH))]^(T)=[20,10,10,10]^(T). 6.The method of claim 5, wherein: ε is equal to
 5. 7. The method of claim1, further comprising: pseudo randomizing rows of said discrete wavelettransformed watermark image before comparing said sequencies.
 8. Themethod of claim 7, wherein: said step of pseudo randomizing rows of saiddiscrete wavelet transformed watermark image generates a pseudorandomization key.
 9. The method of claim 1, further comprising:extracting said watermark from a watermarked host image includingdiscrete wavelet transforming said watermarked image, for each sub-bandsubb selected from the set including LL, LH, HL and HH of said firstpredetermined transform level of the watermarked host image calculatinga weight factor Ŝ as follows:Ŝ(Ĥ _(—) R _(subb)(i,j)=(2*√{square root over (K _(subb)*abs(Ĥ _(—) R_(subb)(i,j)))}+Ĝ _(subb)(i,j), where:Ĝ _(subb)(i,j)={2*√{square root over (max(Ĥ _(—) R _(subb)(i,j)*K_(sub))}+ε}; Ĥ_R_(subb)(i,j) is the autocorrelation of the pixel(i,j) ofthe wavelet transformed host image sub-band Ĥ_subb; and ε is apredetermined constant, determining individual pixels (i,j) of anextracted wavelet domain watermark image from M_(subb)(i,j),N_(subb)(i,j), R_(subb)(i,j) and D_(subb) as follows:If ((D _(subb)>0 AND M _(subb) <D _(subb) >N _(subb)) OR (D _(subb)<0AND R _(subb) <D _(subb) >N _(subb))Then Ŵ_subb(ƒ _(subb)(i),j)=1Else Ŵ_subb(ƒ _(subb)(i),j)=0 where: $\begin{matrix}{T_{1} = {0.75\mspace{14mu}{and}}} \\{T_{2} = 1.25} \\{{M_{sub}\left( {i,j} \right)} = {\left( {T_{1} + {0.75*\Delta\;\hat{H}{\_ R}_{sub}\left( {i,j} \right)}} \right)/2}} \\{{N_{subb}\left( {i,j} \right)} = {\left( {{5*T_{2}} + {0.75*\Delta\hat{H}{\_ R}_{subb}\left( {i,j} \right)}} \right)/2}} \\{{{R_{subb}\left( {i,j} \right)} = {\left( {T_{1} - {0.75*\Delta\hat{H}{\_ R}_{subb}\left( {i,j} \right)}} \right)/2}};{and}}\end{matrix}$${D_{subb} = \frac{{abs}\left( {{\hat{H}{\_ subb}\left( {i,j} \right)} - {{H\_ subb}\left( {i,j} \right)}} \right)}{\alpha_{subb}*{\hat{S}\left( {\hat{H}{\_ R}_{subb}\left( {i,j} \right)} \right.}}},{and}$ inverse discrete binary wavelet transforming the extracted waveletdomain watermark image thereby forming an extracted watermark image. 10.The method of claim 9, further comprising: modeling the effect ofattacks on the watermarked host image and deciding threshold values inthe extraction as follows:ΔĤ _(—) R _(subb)(i,j)=Ĥ _(—) R _(subb)(i,j)*H _(—) R _(subb)(i,j)where: H_R_(subb)(i,j) is the autocorrelation of the pixel(i,j) of thewavelet transformed host image sub-band H_subb.
 11. The method of claim9, wherein: ε is equal to
 5. 12. The method of claim 9, furthercomprising: pseudo randomizing rows of said discrete wavelet transformedwatermark image before comparing said sequencies and generating a pseudorandomization key; and said step of extracting said watermark from awatermarked host image includes reverse pseudo randomizing rows of theextracted wavelet domain watermark image using said pseudo randomizationkey before inverse discrete wavelet transforming the extracted waveletdomain watermark image.
 13. The method of extracting a watermark from awatermarked host image comprising the steps of: discrete wavelettransforming said watermarked image, for each sub-band subb selectedfrom the set including LL, LH, HL and HH of said first predeterminedtransform level of the watermarked host image calculating a weightfactor Ŝ as follows:Ŝ(Ĥ _(—) R _(subb)(i,j)=(2*√{square root over (K _(subb)*abs(Ĥ _(—) R_(subb)(i,j)))}+Ĝ _(subb)(i,j), where:Ĝ _(subb)(i,j)={2*√{square root over (max(Ĥ _(—) R _(subb)(i,j)*K_(sub))}+ε}; Ĥ_R_(subb)(i,j) is the autocorrelation of the pixel(i,j) ofthe wavelet transformed host image sub-band Ĥ_subb; and ε is apredetermined constant, determining individual pixels (i,j) of anextracted wavelet domain watermark image from M_(subb)(i,j),N_(sub)(i,j), R_(sub)(i,j) and D_(subb) as follows:If ((D _(subb)>0 AND M _(subb) <D _(subb) >N _(subb)) OR (D _(subb)<0AND R _(subb) <D _(subb) >N _(subb))Then Ŵ_subb(ƒ _(subb)(i),j)=1Else Ŵ_subb(ƒ _(subb)(i),j)=0 where: $\begin{matrix}{T_{1} = {0.75\mspace{14mu}{and}}} \\{T_{2} = 1.25} \\{{M_{sub}\left( {i,j} \right)} = {\left( {T_{1} + {0.75*\Delta\;\hat{H}{\_ R}_{sub}\left( {i,j} \right)}} \right)/2}} \\{{N_{subb}\left( {i,j} \right)} = {\left( {{5*T_{2}} + {0.75*\Delta\hat{H}{\_ R}_{subb}\left( {i,j} \right)}} \right)/2}} \\{{{R_{subb}\left( {i,j} \right)} = {\left( {T_{1} - {0.75*\Delta\hat{H}{\_ R}_{subb}\left( {i,j} \right)}} \right)/2}};{and}}\end{matrix}$${D_{subb} = \frac{{abs}\left( {{\hat{H}{\_ subb}\left( {i,j} \right)} - {{H\_ subb}\left( {i,j} \right)}} \right)}{\alpha_{subb}*{\hat{S}\left( {\hat{H}{\_ R}_{subb}\left( {i,j} \right)} \right.}}},{and}$ inverse discrete binary wavelet transforming the extracted waveletdomain watermark image thereby forming an extracted watermark image. 14.The method of claim 13, further comprising: modeling the effect ofattacks on the watermarked host image and deciding threshold values inthe extraction as follows:ΔĤ _(—) R _(subb)(i,j)=Ĥ _(—) R _(subb)(i,j)*H _(—) R _(subb)(i,j)where: H_R_(subb)(i,j) is the autocorrelation of the pixel(i,j) of thewavelet transformed host image sub-band H_subb.
 15. The method of claim13, wherein: ε is equal to
 5. 16. The method of claim 13, furthercomprising: reverse pseudo randomizing rows of the extracted waveletdomain watermark image using a pseudo randomization key before inversediscrete binary wavelet transforming the extracted wavelet domainwatermark image.